SSL Notes 4/27
Notes today: Sam
Notes Thursday: Emilie
Snacks Thursday: Carl
Notes Tuesday: Brendan
Snacks Tuesday: Sam
We go over the works-in-progress of the various groups.
Newton's Method paper:
Various edits:
Change R to C as the field we are working over.
Modify equations 2a) and 2b) (to reflect eq. (15)).
We discuss the presentation of the numerator of eq. (15).
Jim makes the point that our result is not useful to numerical analysts,
so we should change of the wording of "Newton's method is uninteresting
as a numerical method" since it *is* interesting to them.
We should have a transitional version of P_n and Q_n in two variables,
be fore stating the noncommutative version.
We discuss the issue of the placement of the recursive definitions of
P_n and Q_n. We should note that C-star refers to the Riemann sphere.
Put the commuting diagram of maps back in.
Move x^(2^n) terms to the front for clarity's sake.
Obtain references for noncommuting q-binomial theorem, Moebius
transformations, Newton's method (either from an elementary calculus
or a dynamics perspective).
Perhaps Knuth? Semi-numerical methods (transposition to non-numerical
methods). We also discuss some features of Paul's write-up on the
"cube-snake" recurrence, which is intended to be a more informal
write-up. There are minor notational and grammatical corrections
which Paul plans on incorporating into subsequent drafts.